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Computing Amplitudes in topological M-theory

TitleComputing Amplitudes in topological M-theory
Publication TypePreprint
AuthorsBonelli, G, Tanzini, A, Zabzine, M
Series TitleJHEP 03 (2007) 023
Document NumberSISSA;74/2006/FM

We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\\\\times S^1$ quantum amplitudes of non-local observables of membranes wrapping the circle reduce to the A-model amplitudes. \\nIn particular for genus zero we show that our model computes the Gopakumar-Vafa invariants. Moreover, for membranes wrapping calibrated homology spheres in the $CY_3$, we find that the amplitudes of our model are related to Joyce invariants.

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